Abstract. We exhibit an intermittency phenomenon in quantum dynamics. More
precisely we derive new lower bounds for the moments of order {\it p}
associated to the state $\psi(t)={\rm e}^{-itH}\psi$ and averaged in
time between $0$ and {\it T}. These lower bounds are expressed in
terms of generalized fractal dimensions $D^\pm_{\mu_\psi}(1/(1+p/d))$ of the
measure $\mu_\psi$ (where {\it d} is the space dimension). This
improves notably previous results, obtained in terms of Hausdorff and
Packing dimension.